Correlation between data sets measures the relationship between data. In other words, it measures how well two sets of data are related. In statistics, the widely used measure of correlation is Pearson Correlation. The full name of this coefficient is Pearson Product Moment Correlation (PMCC). This coefficient indicates a linear relationship between two data sets.

In other words, we can say that this coefficient answers the simple question below:

Am I able to draw a graph to represent the data?

Two letters are employed to depict the Pearson correlation. The Greek letter rho (p) depicts the population and the letter "r" represents the sample.

In the next section of the article, we will discuss the product-moment correlation coefficient (PMCC) in more detail.

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What is the Product Moment Correlation Coefficient (PMCC)?

The product-moment correlation coefficient (PMCC) is a means by which we give a numerical value to the linear correlation of bivariate data. A letter is used to denote the sample's PMCC.

  • There can be any value of r such that
  • If r has a positive value, then it shows that there is a positive correlation between the variables. A positive correlation between variables exists if one variable increases as another variable increases or one variable decrease with the decrease in another variable
  • If "r" has a negative value, then it is indicative of the negative correlation between the variables. A negative correlation between variables exists if one variable increases with the decrease in another variable or vice versa.
  • If the value of "r" is equal to zero, then it indicates that there is no correlation between the variables
  • If the value of "r" is equal to 1 or -1, then it shows that there is a perfect positive or perfect negative correlation between the two variables.
  • If the value of r is closer to 1 or -1, then it shows that there is a strong correlation between the given variables
2-5-1-pmcc-diagram-1
Regression lines on the graph - Image Source: Save my exams

In the next section of the article, we will discuss how to calculate the product mean correlation coefficient.

How to Calculate Product Mean Correlation Coefficient?

You should learn how to utilize your scientific calculator to compute the value of the product mean correlation coefficient (PMCC).  Each calculator has a different method to calculate the PMCC value, hence you should learn how to use your calculator to get the required value.

For this, you need to ensure that your calculator is in statistics mode. You will have the option to turn the frequency on or off. When the statistics mode will be switched "on" on your calculator, you will have a statistics option which will be followed by a regression option in the form A + BX.

On your calculator, you will have two columns, into which you can insert x and y values. After you have input all the values into your calculator, you need to select "r" value from the "STAT" option.

In the next section of the article, we will discuss how to compute PMCC value in scientific and graphical calculators step by step.

Calculating PMCC Values in Scientific and Graphical Calculators

Using the Scientific Calculator

In this section, we will learn how to calculate the product-moment correlation coefficient (PMCC) of the bivariate data using a scientific calculator. Alternatively, you can watch the tutorial below which shows how to use a scientific calculator to calculate PMCC.

Watch How to Use Scientific Calculator to Calculate PMCC

We have also elaborated steps below for your ease.

Steps to Calculate PMCC Using a Scientific Calculator

Follow the steps below to calculate the product-moment correlation coefficient using a scientific calculator.

  • Step 1: From the main menu, go into the statistics mode. Press menu option "6"
Screenshot 1: scientific calc
  • Step 2: Since the PMCC depicts the linear correlation between the two variables, hence press "2" to select  "y = a + bx"
Screenshot 2: scientific calc
  • Step 3: After you press 2, you will get a table in which you can enter "x" and "y" values
Screenshot 3: scientific calc
  • Step 4: Enter the values in the "x" column. After entering each value, press "=" button to press the next value
screenshot 4: scientific calc
  • Step 5: To enter the values in the "y" column, press the right directional button, followed by down button
Screenshot 5: scientific calc
  • Step 6: Now, look at the top left corner of the calculator and press "OPTN". You will get a list of options on the calculator.
Screenshot 6: scientific calc
  • Step 7: Now, press "4" which is a "Regression Calc" option
screenshot 7: scientific calc
  • Step 8: You can now see the values of a, b and r. "r" depicts the value of PMCC
Screenshot 8: scientific calc

In the next section of the article, we will discuss how to use a graphical calculator to compute the value of PMCC.

Using the Graphical Calculator

In this section, we will see how to calculate the product-moment correlation coefficient (PMCC) of the bivariate data using a graphical calculator. Alternatively, you can watch the tutorial below which shows how to use graphical calculator to calculate PMCC.

Watch How to Use Graphical Calculator to Calculate PMCC

Like the scientific calculator section, we have also described the steps below:

Steps to Calculate PMCC Using a Graphical Calculator

  • Step 1: From the main menu, go into the statistics mode. Press menu option "2"
Screenshot 1: graphical calc
  • Step 2: Now, you will have a table on your calculator where you will enter the data. Enter the values by typing in each value, followed by "EXE" button
Screenshot 2: graphical calc
  • Step 3: To enter the values in the second column, press the right directional button on your calculator. Start entering the values in the same way as you have entered into the first column, i.e. by typing in each value and pressing the "EXE" button
Screenshot 3: graphical calc
  • Step 4: To calculate the PMCC value,, press "F2" button on your calculator. [Before you complete any calculation, it is advised to check the settings. Hence, press F6. Since we are dealing with a bivariate data, hence we need to verify that 2 variable calculations "x" variable is stored in list 1 and "y" variable is stored in list 2 with the frequency of 1 in each entry]. This should look like below:
Screenshot 4: Graphical calc

 

  • Step 5: Once you have verified the settings, press "EXIT" button on your calculator to go back
  • Step 6: PMCC calculation is found on the "REG" calculation option. So, press "F3" button
Screenshot step 6: graphical calc
  • Step 7: Since PMCC is related to linear regression, hence press "F1" afterwards.
Screenshot 7: graphical calc
  • Step 8: You will get two options on your calculator screen which will be ax + b and a + bx. From these two options, press "F2" to select y = a + bx
Screenshot 8: graphical calc
  • Step 9: You can now see different values on your calculator screen related to linear regression. The PMCC is denoted by "r".
Screenshot 9: graphical calc

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Emma

Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.